Two motorcycles are traveling due east with different velocities. however, 3.49 seconds later, they have the same velocity. during this 3.49-second interval, motorcycle a has an average acceleration of 2.52 m/s2 due east, while motorcycle b has an average acceleration of 17.5 m/s2 due east. (a) by how much did the speeds differ at the beginning of the 3.49-second interval, and (b) which motorcycle was moving faster?

(a) The speeds differ by 52.2802 m/s at the beginning of 3.49 s interval

(b) The first motorcycle was moving faster

Explanation:

The time of the 2 motorcycles is 3.49 seconds

The final velocities of them are equal

The travelling on the same direction (due east)

The acceleration of the first one is 2.52 m/s²

The acceleration of the second one is 17.5 m/s²

(a)

we need to find the difference between their speeds at the beginning

of the 3.49 s interval

Assume that their final velocity is v

→ v = + t

→ v = + t

→ = 2.52 m/s² , = 17.5 m/s² , t = 3.49 s

- Substitute these value in the equations above

→ v = + (3.49)

  v = + 8.7948 ⇒ (1)

→ v = + (3.49)

  v = + 61.075 ⇒ (2)

Equate equations (1) and (2)

→ + 8.7948 = + 61.075

Subtract 8.7948 from both sides

→ = + 52.2802

Subtract from both sides

→ - = 52.2802 m/s

The speeds differ by 52.2802 m/s at the beginning of 3.49 s interval

(b)

The difference between the speed of the 1st motorcycle and the speed

of the 2nd motorcycle is positive then the 1st motorcycle was moving

faster

The first motorcycle was moving faster

1) Yes

2)

Explanation:

1)

To solve this part, we have to calculate the pressure at the depth of the batyscaphe, and compare it with the maximum pressure that it can withstand.

The pressure exerted by a column of fluid of height h is:

where

is the atmospheric pressure

is the fluid density

is the acceleration due to gravity

h is the height of the column of fluid

Here we have:

is the sea water density

h = 5440 m is the depth at which the bathyscaphe is located

Therefore, the pressure on it is

Since the maximum pressure it can withstand is 60 MPa, then yes, the bathyscaphe can withstand it.

2)

Here we want to find the force exerted on the bathyscaphe.

The relationship between force and pressure on a surface is:

where

p is hte pressure

F is the force

A is the area of the surface

Here we have:

is the pressure exerted

The bathyscaphe has a spherical surface of radius

r = 3 m

So its surface is:

Therefore, we can find the force exerted on it by re-arranging the previous equation: